Array modifier - spiral
Unless, for some reason, you need your dominoes to be an array, one approach, as mentioned, is to start with an Archimedean spiral curve, and use dupliframes. A curve deform modifier will deform your dominoes.

In User Preferences (CtrlAltU) &gt; Add-ons,  enable Add Curve: Extra Objects.

Create and adjust an Archimedean spiral, as a NURBS curve.

Arrange your domino so its origin is at the point you would like the lie on the curve, and, for convenience, so that its 'forward' face looks down global Y.

In the curve's properties, 'Data' tab, check 'Path Animation' and inside that panel, 'Follow'.

Select the domino, then the curve, setting the curve to be the domino's parent. (CtrlP)

In the domino's Properties, 'Object' tab &gt;  'Duplication', select 'Frames', setting 'Start' and 'End' to adjust the region of the spiral over which the domino is to be duplicated. Uncheck 'Speed'


The frequency of dominoes on the curve can be adjusted by the total number of frames in the curve's Path Animation.
Other tweaks available, as per manual.

To convert the duplicate dominoes into linked instances: select the dupli-domino, ShiftCtrlA .. (Make Duplicates Real).
To unlink the object data, and make independent meshes: select the instances, hit U .. (Make Single User). From the Toolbar, check the options 'Object' and 'Object Data'.
UPDATE for Blender 2.8:
Now 'DupliFrames' have gone, another approach is to create a carrier for your duplicate object, whose distortion you don't care about.

Create the spiral curve as before
Create a small plane, same origin, say, up in Z
Assign the plane an Array modifier, constant offset, count set to 'Fit Curve', targeted on the spiral.
Also give the plane a Curve modifier, targeted on the spiral, deformation direction Z.

(left, illustrated)


Now you can create a domino. Its Z will face down the plane's normal..
.. when you parent the domino to the plane, and in the plane's Properties &gt; Object tab &gt; Instancing panel, set 'Faces'.

If, for example, you wanted variations in transform, or a variety of objects on the spiral, you could use the modified plane as a Particle emitter, one per face, instead.
Edit: (response to comment from @Ron Jensen) To make the domino duplis into a real object, to use as a Boolean Cutter..

Arrayed Plane selected, CtrlA &gt; 'Make Instances Real'

CtrlJ Join selected instances of the domino into a new object, and use as a cutter.


I haven't found a way of cutting with a collection instance, which would have been nice, to save data?